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\urldef{\mailsa}\path|{shengbo.guo}@xrce.xerox.com|
\urldef{\mailsb}\path|{scott.sanner, wray.buntine}@nicta.com.au|
\urldef{\mailsc}\path|{thore.graepel}@microsoft.com|
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\begin{document}

\title{Bayesian Score-Based Skill Learning}

% \subtitle{Do you have a subtitle?\\ If so, write it here}

%\titlerunning{Short form of title}        % if too long for running head

\author{Shengbo Guo \and Scott Sanner \\
			  Thore Graepel \and Wray Buntine}
%\author{Unknown authors}
%
\authorrunning{S. Guo, S. Sanner, T. Graepel, W. Buntine}

%\institute{Xerox Research Centre Europe
%\and NICTA and the Australian National University
%\and Microsoft Research Cambridge}


\institute{Shengbo Guo \at
              Xerox Research Centre Europe \\
              % Tel.: +123-45-678910\\
              % Fax: +123-45-678910\\
              \email{shengbo.guo@xrce.xerox.com}           %  \\
%             \emph{Present address:} of F. Author  %  if needed
           \and
           Scott Sanner \at
              NICTA and ANU \\
              \email{scott.sanner@nicta.com.au}
           \and
           Thore Graepel \at
           		Microsoft Research Cambridge \\
           		\email{thore.graepel@microsoft.com}
           \and
           Wray Buntine  \at
              NICTA and ANU \\
              \email{wray.buntine@nicta.com.au}
}

\date{Received: date / Accepted: date}
% The correct dates will be entered by the editor


\maketitle

\begin{abstract}
\input abstract.tex
\keywords{variational inference, matchmaking, graphical models}

% \PACS{PACS code1 \and PACS code2 \and more}
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\end{abstract}

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\section{Introduction}
\input introduction.tex

%%
\section{Skill Learning using TrueSkill}
\input trueskill.tex

%%
\section{Score-based Bayesian Skill Models}
\label{sec:PoissonGaussianModels}
\input model.tex

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\section{Skill and Win/Lose/Draw Probability Inference}
\input inference.tex

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\section{Empirical Evaluation}
\input experiment.tex

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\section{Related Work}
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%%
\section{Conclusion}
\input conclusion.tex

\begin{acknowledgements}
We thank Marconi Barbosa, Guillaume Bouchard, David Stern and Onno Zoeter for interesting discussions, and we also thank the anonymous reviewers at ECML-PKDD'12 for their constructive comments, which help to improve the paper. NICTA is funded by the Australian Government as represented by the Department of Broadband, Communications and the Digital Economy and the Australian Research Council through the ICT Centre of Excellence program.
\end{acknowledgements}



% BibTeX users please use one of
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%\newpage
%\appendix{{\normalsize Appendix}}
%\section{Exponential Integral}
%\label{app:exponentialIntegral}
%Suppose that $x$ is a random variable with Gaussian distribution, i.e., $p(x):=\mathcal{N}(x; \mu, \sigma^2)$, we present the derivations of the expectation for the $\exp(x)$ w.r.t. $x$ as follows:
%\begin{align*}
%    &E_{x\sim p(x)}(\exp(x)) =\int_{x} \frac{\exp(x)}{\sqrt{2\pi \sigma^2}} \exp\left(-\frac{(x-\mu)^2}{2\sigma^2}\right)\mathrm{d}x \\
%    &=\frac{1}{\sqrt{2\pi \sigma^2}} \exp\left(-\frac{\mu^2}{2\sigma^2}\right)\int_{x} \exp\left(-\frac{x^{2}-2x(\mu+\sigma^2)}{2\sigma^2}\right)\mathrm{d}x \\
%    %&=\frac{1}{\sqrt{2\pi \sigma^2}} \exp\left(-\frac{\mu^2}{2\sigma^2}\right) \exp\left(\frac{(\mu+\sigma^2)^2}{2\sigma^2}\right) \int_{x} \exp\left(-\frac{(x-(\mu+\sigma^2))^2}{2\sigma^2}\right)dx\\
%    &=\frac{1}{\sqrt{2\pi \sigma^2}} \exp\left(\mu + \frac{\sigma^2}{2}\right) \int_{x} \exp\left(-\frac{(x-(\mu+\sigma^2))^2}{2\sigma^2}\right)\mathrm{d}x\\
%    &=\frac{1}{\sqrt{2\pi \sigma^2}} \exp\left(\mu + \frac{\sigma^2}{2}\right) \sqrt{2\pi \sigma^2 } \\
%    &=\exp(\mu+\sigma^2/2).
%\end{align*}
%
%\section{Log Gaussian Integral}
%\label{app:logGaussianIntegral}
%Suppose $x$ is a random variable with Gaussian distribution $p(x): \mathcal{N}\sim(\mu, \sigma^2)$ and $q(x)$ is a Gaussian, $\mathcal{N}\sim(\mu_1, \sigma_1^2)$, let us show how to derive the expectation of $\log q(x)$ w.r.t. $x$ as follows:
%\begin{align*}
%    &E_{x\sim p(x)}( \log q(x) ) =E_{x \sim p(x)} \left(\log\left(\frac{1}{\sqrt{2\pi\sigma_1^2}}\exp\left(-\frac{(x-\mu_1)^2}{2\sigma_1^2}\right)\right)\right)\\
%   &= -\frac{1}{2}\log(2\pi\sigma_{1}^2) - \frac{1}{2\sigma_{1}^2}E_{x\sim p(x)}( x-\mu_{1} )^2 \\
%    &= -\frac{1}{2}\log(2\pi\sigma_{1}^2) - \frac{1}{2\sigma_{1}^2}\left(E_{x\sim p(x)}( x^2 )-2\mu_1\mu + \mu_{1}^2 \right) \\
%    &= -\frac{1}{2}\log(2\pi\sigma_{1}^2) - \frac{1}{2\sigma_{1}^2}\left(\sigma^2 + \mu^2-2\mu_1\mu + \mu_{1}^2 \right).
%\end{align*}

\end{document}
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